Counterdiabatic driving of the quantum Ising model

TL;DR

This paper derives an exact formula for counterdiabatic driving in the quantum Ising model, enabling rapid adiabatic-like evolution and analyzing the effects of quantum criticality on finite-size systems.

Contribution

It provides a closed-form expression for the counterdiabatic Hamiltonian coefficients in the quantum Ising model and evaluates approximate methods for state preparation.

Findings

Exact counterdiabatic Hamiltonian coefficients derived.

Approximate methods' efficiency in state preparation analyzed.

Quantum criticality amplifies finite-size effects in counterdiabatic dynamics.

Abstract

The system undergoes adiabatic evolution when its population in the instantaneous eigenbasis of its time-dependent Hamiltonian changes only negligibly. Realization of such dynamics requires slow-enough changes of the parameters of the Hamiltonian, a task that can be hard to achieve near quantum critical points. A powerful alternative is provided by the counterdiabatic modification of the Hamiltonian allowing for an arbitrarily quick implementation of the adiabatic dynamics. Such a counterdiabatic driving protocol has been recently proposed for the quantum Ising model [A. del Campo et al., Phys. Rev. Lett. 109, 115703 (2012)]. We derive an exact closed-form expression for all the coefficients of the counterdiabatic Ising Hamiltonian. We also discuss two approximations to the exact counterdiabatic Ising Hamiltonian quantifying their efficiency of the dynamical preparation of the desired ground state. In particular, these studies show how quantum criticality enhances finite-size effects in the counterdiabatic dynamics.